In the  figure  above the vertical deviations of the individual points  from the  line are shown  as the short vertical lines joining  the points  to the least  squares line. These deviations will be  denoted by the symbol the value of e varies from  one  point to another.  In some  cases it is  positive in others it is negative. If  the line  drawn happens to be the least squares line  then the  value of ∑e2 is the least possible. It  is because  of this  feature the methods is known  as least  squares methods.

Why  we insist  on minimizing  the sum  of squared  deviations is a  question that  needs explanation. It  we denote  the deviation from  the actual  value y to  estimated value (Y - Y )or e it is logical that we  want the  ∑ ( Y-Y) or ∑ e to be as small  as possible  however  mere examining ∑ ( Y-Y) or ∑ e  is inappropriate since  any e can be positive or negative and large positive  value  and large  negative  values  could cancel one another out. But  large values of e regardless of their  sign  indicate   a poor  prediction. Even  if we  ignore  the sings while working  out ∑e  the difficulties may continue to  be there . hence the standard procedure is to eliminate the effect of sings by squaring each observation. Squaring each  term  accomplishes two purposes viz.